We all know that while you dream you "see" images and simulations of the real world
As impressive as that is by itself, I have a question
What do we actually see while we dream?
If you were to take a mental "picture" of what you see in your dreams, and print it on paper
If you were to look at that same image while you were awake, would it still look like an image of something familiar?
Or just a bright splotch of colors and lights
Or maybe nothing at all?

Bluedrake wrote: But wouldn't you find it intriguing if it did in fact make sense in both?
I think that could make quite an impact on how we view the brains ability to simulate an environment

I think it's a lot more intriguing when it only appears to make sense in the Dream world, for it is beyond your current comprehension of things.
The Brain is a very interesting organ indeed, some of it's functions are very mysterious and complicated.

However, why do we think? Why do we have dreams? Why are we not some some very basic action-and-reaction organisms?
When did somewhere in the evolutionary chain we stopped being "brainless" beings and started to actually think? It's easy to believe that in the primitive versions of humankind, it was developed the method of thinking, and it helped the individual to survive the environment. Was it on purpose? Was it a coincidential mutation on the DNA? Either way, we managed to figure out that killing that animal with that hard object called rock was a lot faster and effective than by using our bare hands. And those who used the rocks and sticks to kill their preys got stronger and survived. It's all about natural selection of things, and the thought and the brain were purely created out of mutations, which accidently lead to greater chances of survival. The dreams and such, would be in my opinion, only a side-effect, therefore anything we imagine in our dreams are purely links we've made to things we've named in the Physical world.

Now your question comes along and wonders, "What about things that make have no link to anything in the real world".
If you read that entire wall of text, you'll realize that the question you've made is far more complicated.

TL;DR: We have acquired some form of mental retardation mutation a long time ago in the evolutionary chain that is not harmful or benefical to our survival, and that mutation makes us see, sometimes, things in our dreams that mean jackshit.

in psychology it's thought that dreams are only the brain making sense of random signals sent by the pons.

There's a fun exercise where you the fleeting moments before you fall asleep, you try to backtrack to how you got to your current thought, often times you can't and the thought itself doesn't make sense at all. our brain still thinks this without any alert going off that your thinking wrong like when you become aware you are doing a math problem incorrectly, our brain for dreaming takes random signals and puts them into context.

Also it is said that while you are dreaming in brain activates problem solving regions, so many scientists think that brain is solving and thinking out some of the problems that occur in physical world...
Also i have this book which is similar to horoscope (all those predictions and stuff) which works based on your dreams, i don't really know if i should believe it or not but it kinda seems to work xD anyways that might also work like, that i dream that i am wielding a sword for example, and then i looked up at the book and it was said that sword (if youre holding it) is a sign of strength and success, after reading all that you're like: bwahaa success, and you feel good and be more positive, and in the end the dream didnt had that much "magical" influence than mere boasting..
so every time i dream something out of ordinary dreaming, like something rather weird and what had a large influence on how i felt in dream (most important stuff from my dream) , i just look it up in the book and find out what could and what could not happen
(the book is 400 pages, in dictionary style, the thing you see in the dream- what did you do with it?- explanations for each action you do)
Most thing in the book arent positive towards you xD
But i kinda only get the good ones, i guess im lucky